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Embeddings of Generalised Morrey Smoothness Spaces 广义Morrey平滑空间的嵌入
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-01-15 DOI: 10.1007/s10114-025-3553-3
Dorothee D. Haroske, Zhen Liu, Susana D. Moura, Leszek Skrzypczak
{"title":"Embeddings of Generalised Morrey Smoothness Spaces","authors":"Dorothee D. Haroske,&nbsp;Zhen Liu,&nbsp;Susana D. Moura,&nbsp;Leszek Skrzypczak","doi":"10.1007/s10114-025-3553-3","DOIUrl":"10.1007/s10114-025-3553-3","url":null,"abstract":"<div><p>We study embeddings between generalised Triebel–Lizorkin–Morrey spaces <span>(cal{E}_{varphi,p,q}^{s}(mathbb{R}^{d}))</span> and within the scales of further generalised Morrey smoothness spaces like <span>(cal{N}_{varphi,p,q}^{s}(mathbb{R}^{d}))</span>, <i>B</i><span>\u0000 <sup><i>s,φ</i></sup><sub><i>p,q</i></sub>\u0000 \u0000 </span>(ℝ<sup><i>d</i></sup>) and <i>F</i><span>\u0000 <sup><i>s,φ</i></sup><sub><i>p,q</i></sub>\u0000 \u0000 </span>(ℝ<sup><i>d</i></sup>). The latter have been investigated in a recent paper by the first two authors (2023), while the embeddings of the scale <span>(cal{N}_{varphi,p,q}^{s}(mathbb{R}^{d}))</span> were mainly obtained in a paper of the first and last two authors (2022). Now we concentrate on the characterisation of the spaces <span>(cal{E}_{varphi,p,q}^{s}(mathbb{R}^{d}))</span>. Our approach requires a wavelet characterisation of those spaces which we establish for the system of Daubechies’ wavelets. Then we prove necessary and sufficient conditions for the embedding <span>(cal{E}_{varphi_{1},p_{1},q_{1}}^{s_{1}}(mathbb{R}^{d})hookrightarrowcal{E}_{varphi_{2},p_{2},q_{2}}^{s_{2}}(mathbb{R}^{d}))</span>. We can also provide some almost final answer to the question when <span>(cal{E}_{varphi,p,q}^{s}(mathbb{R}^{d}))</span> is embedded into <i>C</i>(ℝ<sup><i>d</i></sup>), complementing our recent findings in case of <span>(cal{N}_{varphi,p,q}^{s}(mathbb{R}^{d}))</span>.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 1","pages":"413 - 456"},"PeriodicalIF":0.8,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New Characterization of Morrey-Herz Spaces and Morrey-Herz-Hardy Spaces with Applications to Various Linear Operators Morrey-Herz空间和Morrey-Herz- hardy空间的新表征及其在各种线性算子上的应用
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-01-15 DOI: 10.1007/s10114-025-3570-2
Kwok Pun Ho, Yoshihiro Sawano
{"title":"New Characterization of Morrey-Herz Spaces and Morrey-Herz-Hardy Spaces with Applications to Various Linear Operators","authors":"Kwok Pun Ho,&nbsp;Yoshihiro Sawano","doi":"10.1007/s10114-025-3570-2","DOIUrl":"10.1007/s10114-025-3570-2","url":null,"abstract":"<div><p>This paper is an offspring of the previous study on Herz spaces. A new characterization of Morrey-Herz spaces is given. As applications, the boundedness of various operators is obtained. For example, higher-order commutators generated by singular integral operators and BMO functions are proved to be bounded on Morrey-Herz spaces. The theory of Morrey-Herz-Hardy spaces is also developed.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 1","pages":"327 - 354"},"PeriodicalIF":0.8,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Remark on Stein–Tomas Type Restriction Theorems 关于Stein-Tomas型约束定理的一个注解
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-01-15 DOI: 10.1007/s10114-025-3525-7
Xiaochun Li
{"title":"A Remark on Stein–Tomas Type Restriction Theorems","authors":"Xiaochun Li","doi":"10.1007/s10114-025-3525-7","DOIUrl":"10.1007/s10114-025-3525-7","url":null,"abstract":"<div><p>A local <i>L</i><sup><i>p</i></sup> estimate is proved by using the <i>σ</i>-uniformity, which is motivated by the study of the Stein–Tomas type restriction theorems and Waring’s problem.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 1","pages":"122 - 130"},"PeriodicalIF":0.8,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108453","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Weighted Estimates for Generalised Conical Square Functions and Applications 广义圆锥平方函数的加权估计及其应用
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-01-15 DOI: 10.1007/s10114-025-3478-x
The Anh Bui, Xuan Thinh Duong, Ji Li
{"title":"Weighted Estimates for Generalised Conical Square Functions and Applications","authors":"The Anh Bui,&nbsp;Xuan Thinh Duong,&nbsp;Ji Li","doi":"10.1007/s10114-025-3478-x","DOIUrl":"10.1007/s10114-025-3478-x","url":null,"abstract":"<div><p>Let <span>({cal{A}_{t}}_{t&gt;0})</span> be a family of bounded linear operator on <i>L</i><sup>2</sup>(<i>X</i>) where (<i>X, d, μ</i>) is a metric space with metric <i>d</i> and doubling measure <i>μ</i>. Assume that the family <span>({cal{A}_{t}}_{t&gt;0})</span> satisfies suitable off-diagonal estimates from <span>(L^{p_{0}})</span> to <i>L</i><sup>2</sup> for some <i>p</i><sub>0</sub> &lt; 2. This paper aims to prove weighted bound estimates for conical square functions and g-functions associated to the family <span>({cal{A}_{t}}_{t&gt;0})</span>. Some applications such as weighted bounds for bilinear estimates associated to certain differential operators are also obtained.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 1","pages":"191 - 208"},"PeriodicalIF":0.8,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Conformal Composition for Borderline Fractional Sobolev Spaces 边界分数Sobolev空间的保角复合
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-01-15 DOI: 10.1007/s10114-025-3649-9
Nijjwal Karak, Pekka Koskela, Debanjan Nandi, Swadesh Kumar Sahoo
{"title":"Conformal Composition for Borderline Fractional Sobolev Spaces","authors":"Nijjwal Karak,&nbsp;Pekka Koskela,&nbsp;Debanjan Nandi,&nbsp;Swadesh Kumar Sahoo","doi":"10.1007/s10114-025-3649-9","DOIUrl":"10.1007/s10114-025-3649-9","url":null,"abstract":"<div><p>We establish a pointwise property for homogeneous fractional Sobolev spaces in domains with non-empty boundary, extending a similar result of Koskela–Yang–Zhou. We use this to show that a conformal map from the unit disk onto a simply connected planar domain induces a bounded composition operator from the borderline homogeneous fractional Sobolev space of the domain into the corresponding space of the unit disk.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 1","pages":"457 - 471"},"PeriodicalIF":0.8,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bilinear Exotic Calderón-Zygmund Operators 双线性奇异Calderón-Zygmund算子
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-01-15 DOI: 10.1007/s10114-025-3589-4
Jin Bai, Jinsong Li, Kangwei Li
{"title":"Bilinear Exotic Calderón-Zygmund Operators","authors":"Jin Bai,&nbsp;Jinsong Li,&nbsp;Kangwei Li","doi":"10.1007/s10114-025-3589-4","DOIUrl":"10.1007/s10114-025-3589-4","url":null,"abstract":"<div><p>We introduce a bilinear extension of the so-called exotic Calderón-Zygmund operators. These kernels arise naturally from the bilinear singular integrals associated with Zygmund dilations. We show that such a class of operators satisfy a <i>T</i>1 theorem in the same form as the standard Calderón-Zygmund operators. However, one-parameter weighted estimates may fail in general, and unlike the linear case, we are not able to provide the end-point estimates in full generality.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 1","pages":"355 - 377"},"PeriodicalIF":0.8,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Interpolation of Closed Ideals of Bilinear Operators 双线性算子的闭理想插值
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-01-01 DOI: 10.1007/s10114-025-3506-x
Fernando Cobos, Luz M. Fernández-Cabrera, Antón Martínez
{"title":"Interpolation of Closed Ideals of Bilinear Operators","authors":"Fernando Cobos,&nbsp;Luz M. Fernández-Cabrera,&nbsp;Antón Martínez","doi":"10.1007/s10114-025-3506-x","DOIUrl":"10.1007/s10114-025-3506-x","url":null,"abstract":"<div><p>We extend the (outer) measure <span>(gamma_{cal{I}})</span> associated to an operator ideal <span>(cal{I})</span> to a measure <span>(gamma_{frak{J}})</span> for bounded bilinear operators. If <span>(cal{I})</span> is surjective and closed, and <span>(frak{J})</span> is the class of those bilinear operators such that <span>(gamma_{frak{J}}(T)=0)</span>, we prove that <span>(frak{J})</span> coincides with the composition bideal <span>(cal{I}circfrak{B})</span>. If <span>(cal{I})</span> satisfies the Σ<sub><i>r</i></sub>-condition, we establish a simple necessary and sufficient condition for an interpolated operator by the real method to belong to <span>(frak{J})</span>. Furthermore, if in addition <span>(cal{I})</span> is symmetric, we prove a formula for the measure <span>(gamma_{frak{J}})</span> of an operator interpolated by the real method. In particular, results apply to weakly compact operators.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 1","pages":"209 - 230"},"PeriodicalIF":0.8,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108139","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Weighted Maximal L2 Estimate of Operator-valued Bochner–Riesz Means 算子值Bochner-Riesz均值的加权极大L2估计
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-01-01 DOI: 10.1007/s10114-025-3315-2
Guixiang Hong, Liyuan Zhang
{"title":"A Weighted Maximal L2 Estimate of Operator-valued Bochner–Riesz Means","authors":"Guixiang Hong,&nbsp;Liyuan Zhang","doi":"10.1007/s10114-025-3315-2","DOIUrl":"10.1007/s10114-025-3315-2","url":null,"abstract":"<div><p>In this paper, we establish a weighted maximal <i>L</i><sub>2</sub> estimate of operator-valued Bochner–Riesz means. The proof is based on noncommutative square function estimates and a sharp weighted noncommutative Hardy–Littlewood maximal inequality.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 1","pages":"78 - 98"},"PeriodicalIF":0.8,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Competing Potentials Effect on Positive Solutions to a Schrödinger-Poisson System 竞争电位对Schrödinger-Poisson系统正解的影响
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-12-26 DOI: 10.1007/s10114-024-3124-z
Haining Fan, Xiaochun Liu
{"title":"Competing Potentials Effect on Positive Solutions to a Schrödinger-Poisson System","authors":"Haining Fan,&nbsp;Xiaochun Liu","doi":"10.1007/s10114-024-3124-z","DOIUrl":"10.1007/s10114-024-3124-z","url":null,"abstract":"<div><p>In this paper, we study the multiplicity and concentration of positive solutions for a Schrödinger-Poisson system involving sign-changing potential and the nonlinearity <i>K</i>(<i>x</i>)∣<i>u</i>∣<sup><i>p</i>−2</sup><i>u</i> (2 &lt; <i>p</i> &lt; 4) in ℝ<sup>3</sup>. Such a problem cannot be studied by variational methods in a standard way, even by restricting its corresponding energy functional on the Nehari manifold since its (PS) sequence may not be bounded. By some new analytic techniques and the Ljusternik-Schnirelmann category theory, we relate the concentration and the number of positive solutions to the category of the global minima set of a suitable ground energy function. Furthermore, we investigate the asymptotic behavior of the solutions. In particular, we do not use Pohozaev equality in this work.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 4","pages":"1055 - 1090"},"PeriodicalIF":0.8,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bi-predual Spaces of Generalized Campanato Spaces with Variable Growth Condition 变生长条件广义Campanato空间的双前偶空间
IF 0.8 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2024-12-20 DOI: 10.1007/s10114-024-3368-7
Satoshi Yamaguchi, Eiichi Nakai, Katsunori Shimomura
{"title":"Bi-predual Spaces of Generalized Campanato Spaces with Variable Growth Condition","authors":"Satoshi Yamaguchi,&nbsp;Eiichi Nakai,&nbsp;Katsunori Shimomura","doi":"10.1007/s10114-024-3368-7","DOIUrl":"10.1007/s10114-024-3368-7","url":null,"abstract":"<div><p>In this paper we extend the duality <span>(({overline{C_{rm comp}^{infty}({mathbb R}^{d})}}^{{rm BMO}({mathbb R}^{d})})^{ast}=H^{1}({mathbb {R}^{d}}))</span> to generalized Campanato spaces with variable growth condition <span>({cal L}_{p,phi}({mathbb R}^{d}))</span> instead of BMO(ℝ<sup><i>d</i></sup>). We also extend the characterization of <span>({overline{C_{rm comp}^{infty}({mathbb R}^{d})}}^{{rm BMO}({mathbb R}^{d})})</span> by Uchiyama (1978) to <span>({overline{C_{rm comp}^{infty}({mathbb R}^{d})}}^{{cal L}_{p,phi}({mathbb R}^{d})})</span>. Moreover, using this characterization, we prove the boundedness of singular and fractional integral operators on <span>({overline{C_{rm comp}^{infty}({mathbb R}^{d})}}^{{cal L}_{p,phi}({mathbb R}^{d})})</span>. The function space <span>({cal L}_{p,phi}({mathbb R}^{d}))</span> treated in this paper covers the case that it is coincide with Lip<sub><i>α</i></sub> on one area, with BMO on another area and with the Morrey space on the other area, for example.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 1","pages":"273 - 303"},"PeriodicalIF":0.8,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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